Per Erik Manne (firstname.lastname@example.org) wrote: > Miguel Lerma wrote: > > Incidentally, the criticism about Hsiang's proof is caused by > > lack of details only in part. It seems that some claims included > > in the "proof" are actually wrong. > > > > Miguel A. Lerma
> This is in fact what Thomas Hales claims in an article in the > Math.Intelligencer (no.3, 1994). Hsiang has answered this criticism > in a later issue (no.1, 1995). I haven't seen any response to > this answer. In this subject I'm sufficiently non-expert to be
Right, Hsiang answered Hales' criticism. I am curious to see if that answer is satisfactory for J.H. Conway, T.C. Hales, D.J. Muder, and N.J.A. Sloane, who expresed their negative opinion in a letter to the editor in The Math. Intell. Vol.16 (1994) N.2. Anyway, we may wonder in what extend a proof that is not convincing for (or understood by) the main world experts in the matter can be actually be considered "a proof".
In inspite that I have expressed some skepticism about "computer proofs", I can see that they may play a role in the future of Mathematics. I agree up to some extend with C.W.H. Lam's opinions in his article "How Reliable Is a Computer-Based Proof?", The Math. Intell. Vol.12 (1990) N.1, pp.8-12. Lam gave a computer based proof that there do not exist any finite projective planes of order 10. The proof used several thousand hours of supercomputer time, and it seems to be impossible to check in the traditional sense of the word. However it can be independently verified. Lam also gives some ideas about how to increase confidence in a computed result.